Introduction to Empirical Processes and Semiparametric Inference by Michael R. Kosorok

By T. Nummi. 2009

634 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b257c05221b901bea41128ee1e2fba098260d6d8

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Citations in the corpus

High-Dimensional Sparse Additive Hazards Regression (2012, background): “10 of Kosorok (2008) that Zj ≡ {Zj (t) : t ∈ [0, τ ]} is a VC-hull class associated with a VC class of index 2. Then, by Corollary 2.6.12 of van der Vaart and Wellner (1996), the entropy of Zj satisfies log N (ε‖F‖Q,2,Zj , L2(Q)) ≤ K ′(1/ε) for some constant K ′ > 0, and hence, Zj has the uniform en”
Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap (2017, methodology): “Λ/ we have lim sup n→∞ P0.μ .h/ <L.h// α 2 and lim sup n→∞ P0.μ .h/ >U.h// α 2 : The proof of this result, which invokes the general theory of the bootstrap for Z-estimators (Wellner and Zhan (1996) and Kosorok (2006), chapter 10), is explained in appendix C in the on-line supplement.”
Bootstrap consistency for general semiparametric $M$-estimation (2009, methodology): “In a recent monograph, Kosorok pointed out that “convergence rate and asymptotic normality results are quite difficult to establish for the nonparametric bootstrap (based on multinomial weights), especially for models with parameters not estimable at the √ n rate” [22].”
Post-Selection Inference for Generalized Linear Models With Many Controls (2013, methodology): “Our model is a special case of a partially linear logistic model, and Kosorok (2008) derived an efficient score function for the latter, Si = {yi − G(diα0 + x ′iβ0)}{di − m∗0(xi)}, where m∗0(xi) = E[widi |xi] E[wi |xi] .”
Inference on Directionally Differentiable Functions (2014, background): “(rn{θ̂∗n − θ̂n} ≤ t|{Xi}ni=1)− P (G0 ≤ t)| = op(1) (30) for any closed subset A of the continuity points of the cdf of G0; see Kosorok (2008).”
Goodness‐of‐fit testing based on a weighted bootstrap: A fast large‐sample alternative to the parametric bootstrap (2012, positive): “To extend the breadth of our study, we shall work in the framework of the theory of empirical processes as presented for instance in van der Vaart and Wellner (2000) or Kosorok (2008).”
The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series (2014, background): “gible in probability from Proposition B2. Hence, we obtain the desired result. (b)From the continuous mapping theorem, the result in (a) of this theorem yields the desired result. See Theorem 10.8 of Kosorok (2007) for a general argument. Proofof Theorem 3. As shown in (A-4), under both ﬁxed and loc”
Quantile Treatment Effects in the Regression Discontinuity Design: Process Results and Gini Coefficient (2010, methodology): “4 in Kosorok (2008) for a denition of the functional delta method and an application to the quantile operator).”
Optimal-order bounds on the rate of convergence to normality in the multivariate delta method (2009, methodology): “The reader is referred to [75] for a rather detailed description of the delta method and its applications; see [39, 71] for a more modern treatment of the delta method applied to infinite-dimensional random vectors.”
The Generalized Oaxaca-Blinder Estimator (2020, background): “Kosorok (2008) and van der Vaart and Wellner (1996) gave a wealth of additional examples.”
Empirical process results for exchangeable arrays (2019, background): “…a.s.−→ 0 and sup F∞ ∣∣∣Pnf2 − Pf2 ∣∣∣ a.s.−→ 0, which finally leads to lim δ↓0 lim sup n→+∞ E ( σ∗2n | (Yi)i∈Ik ) = 0 a.s. 1.4 Theorem 2.3 The proof is the same as that of Theorem 13.4 in Kosorok (2006), with one change only: we have to check that G, the limit of θ 7→ √n(Ψn(θ)−Ψ(θ)), is continuous.”
A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results (2017, methodology): “ach avoids the need to work with the seemingly awkward notion of \conditional law" of a non-measurable function. Focusing for instance on existing continuous mapping theorems for the bootstrap (Kosorok, 2008, Section 10.1.4), it appears that, for transferring Assertion (c) of Lemma3.1into Asser”
New estimators of the Pickands dependence function and a test for extreme-value dependence (2011, methodology): “Hence, the result follows by the continuous mapping theorem for the bootstrap [see, e.g., Theorem 10.8 in Kosorok (2008)] provided the conditional weak convergence in (4.4) holds under the nonrestrictive smoothness assumption (3.6).”